🚀 go-pugleaf

In article <2861@optima.cs.arizona.edu> gudeman@cs.arizona.edu (David Gudeman) writes:

|If you want to get theoretical, then you can _theoretically_ keep
|buying tapes until the world's supply of tape runs out.  Then you can
|manufacture more.  When you use up all the earth's supply of materials
|for making tapes, you can build mining space ships.  The question of
|whether a computer is a finite-state device or not boils down to the
|question of whether the universe holds a finite amount of material for
|making tape.  In this case whether you believe that a computer is a
|finite-state device depends on whether you believe there is a finite
|amount of matter in the universe.

There is definitely and without question a finite amount of matter in
the universe that I am willing to make tapes out of.

For more than a finite amount of matter to become available to us on a
timescale in which we are in an energetic position to make some use of
it, would require certain (IMHO unlikely) breakthroughs in physics.

|The question of whether an electronic computer is an FSA or an
|infinite-state device is not as trivial as most people seem to think.

Evidently, I disagree. I am PERSONALLY willing to engineer my
compilers on the assumption that (a) FTL travel, (b) many-worlds
parallelism and (c) anything comparably revolutionary will not become
available within the useful lifetime of the software.

And even WITH those breakthroughs, I still think computers would for
the most part remain finite, making finite computation a useful field
of research.
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stephen p spackman         Center for Information and Language Studies
systems analyst                                  University of Chicago
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In article <2861@optima.cs.arizona.edu> gudeman@cs.arizona.edu (David Gudeman) writes:
>Keep in mind that "state" in this sense refers to the entire body of
>information accessible by the computer.  If a computer runs out of
>storage, you can always go buy another tape.  Now there are two
>possible ways to interpret the question of whether this gives the
>computer unbounded storage: the practical and the theoretical.
>
>Whether this gives the computer _practical_ unbounded store depends on
>your opinion of what is practical.  If either you don't expect your
>problems to run out of tape, or your problems are important enough
>that you are willing to keep the computer supplied with all the tape
>it needs, then the computer has a practically unbounded state space.
>If you don't agree that the above is practical, then the computer has
>a _practically_ bounded state space.
>

Corret me if I'm wrong, but it seems as if proving that a program
will require at least the lifetime of the solar system to finish
computing on a device that switches in the time it takes an electron
to move 1 smallest measurable quanta, would be sufficient for most
practical purposes. 

>If you want to get theoretical, then you can _theoretically_ keep
>buying tapes until the world's supply of tape runs out.  Then you can

Of course, but now you are asking for a mathematical model which takes
your behavior into account. This is a rather more involved question than
the one we started with.

David Gudeman says:

   If you want to get theoretical, then you can _theoretically_ keep
   buying tapes until the world's supply of tape runs out.  Then you can
   manufacture more.  When you use up all the earth's supply of materials
   for making tapes, you can build mining space ships.  

Careful, David; maybe the material for tapes is also an essential part of the
mining ships. What do you do if you can't build the ship because the last
gramme of poly-unobtainable-thene, needed for the scrawlbar-widget on the
pilots desktop, has just been used to record a Very Significant Digit of the
answer (maybe the ships flight plan ...)?

Resource allocation is hard.

--

Regards, Kers.      | "You're better off  not dreaming of  the things to come;
Caravan:            | Dreams  are always ending  far too soon."

In article <KERS.91May13111546@cdollin.hpl.hp.com>, kers@hplb.hpl.hp.com (Chris Dollin) writes:
> Careful, David; maybe the material for tapes is also an essential part of the
> mining ships. What do you do if you can't build the ship because the last
> gramme of poly-unobtainable-thene, needed for the scrawlbar-widget on the
> pilots desktop, has just been used to record a Very Significant Digit of the
> answer (maybe the ships flight plan ...)?

This one has already been answered in this newsgroup, this year.
You use space itself as your store (think "delay-line").
Your ground station transmits a string of pulses, N per second,
to a space-ship D metres away, which simply reflects them back
to the ground station.  The total distance travelled is 2D, at
a round-trip time of 2D/c seconds, so space holds 2ND/c pulses.
When you want more storage, you just move the spaceship further
away.  You can have as much storage as you want, if you're willing
to wait for it.  Have you read the SF story "the Very Slow Time
Machine"?  This is a Very Slow Turing Machine.

-- 
There is no such thing as a balanced ecology; ecosystems are chaotic.